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Some Problems Involving Circular and Spherical Targets

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  • George Marsaglia

    (Boeing Scientific Research Laboratories, Seattle, Washington)

Abstract

This article is concerned with some problems that occur in certain tactical considerations: how should one place k circles [spheres] in the plane [3-space] so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles [spheres]. For k > 3 the problem seems hopeless, (except for certain special situations); the case for k = 3 is still unresolved and is being worked on by a number of investigators, and the case for k = 2 is solved completely in this paper. The results for k = 2 have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for k ≧ 3.

Suggested Citation

  • George Marsaglia, 1965. "Some Problems Involving Circular and Spherical Targets," Operations Research, INFORMS, vol. 13(1), pages 18-27, February.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:1:p:18-27
    DOI: 10.1287/opre.13.1.18
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